Electrical Circuits Lab Series RC Circuit Phasor Diagram

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1 Electrical Circuits Lab Series RC Circuit Phasor Diagram - Simple steps to draw phasor diagram of a series RC circuit without memorizing: * Start with the quantity (voltage or current) that is common for the resistor R and the capacitor C, which is here the source current I (because it passes through both R and C without being divided). Figure (1) Series RC circuit * Now we know that I and resistor voltage V R are in phase or have the same phase angle (there zero crossings are the same on the time axis) and V R is greater than I in magnitude. * Since I equal the capacitor current I C and we know that I C leads the capacitor voltage V C by 90 degrees, we will add V C on the phasor diagram as follows: * Now, the source voltage V S equals the vector summation of V R and V C : Figure (2) Series RC circuit Phasor Diagram

2 - Important notes on the phasor diagram of series RC circuit shown in figure (2): A- All the vectors are rotating in the same angular speed ω. B- This circuit acts as a capacitive circuit and I leads V S by a phase shift of Ө (which is the current angle if the source voltage is the reference signal). Ө ranges from 0 o to 90 o (0 o < Ө <90 o ). If Ө=0 o then this circuit becomes a resistive circuit and if Ө=90 o then the circuit becomes a pure capacitive circuit. C- The phase shift between the source voltage and its current Ө is important and you have two ways to find its value: a- b- = - = - D- Using the phasor diagram, you can find all needed quantities in the circuit like all the voltages magnitude and phase and all the currents magnitude and phase. For a series RC circuit, if the magnitude of V C and V R was measured in Lab. (as a peak value from an oscilloscope or rms value from a digital multimeter), then we can find the magnitude of V S as follows: E- You can find all leading or lagging voltages and currents in this circuit with respect to a reference signal like the source voltage V S. For example, it is clearly shown by the phasor diagram that I leads V S by Ө degrees, V R leads V S by Ө degrees (since it is in phase with I) and V C lags V S by 90 o - Ө. F- The phasor diagram helps in finding the change in current and voltage (magnitude and phase) with voltage source frequency f changing. With frequency f increasing, the capactive reactance X C will decrease and V C will decrease too, the the resistor R will not be affected by the change of f, then by voltage

3 division rule V R will increase (to prevent V S from changing since V S is a voltage source). Since X C decrease and R is constant the total impedance Z will decrease and the source current I will increase. and will decrease because from 0 to 90 o. In a concise way: f X C Z I V R V C Ө. and the tan -1 function is increasing on the interval G- Figure (3) below shows a time domain representation for all the vectors shown on the phasor diagram: Figure (3) Series RC Circuit Time Domain Representation

4 Electrical Circuits Lab Parallel RC Circuit Phasor Diagram - Simple steps to draw phasor diagram of a parallel RC circuit without memorizing: * Start with the quantity (voltage or current) that is common for the resistor R and the capacitor C, which is here the source Voltage V S (because it is parallel with both R and C without being divided). Figure (1) Parallel RC circuit * Now we know that resistor current I R and resistor voltage V R (which equals V S ) are in phase or have the same phase angle (there zero crossings are the same on the time axis) and V R is greater than I R in magnitude. * Since V S equal the voltage V C and we know that V C lags the capacitor current I C by 90 degrees, we will add I C on the phasor diagram as follows: * Finally, the source current I equal the vector summation of I R and I C : Figure (2) Parallel RC circuit Phasor Diagram

5 - Important notes on the phasor diagram of Parallel RC circuit shown in figure (2): A- All the vectors are rotating in the same angular speed ω. B- This circuit acts as a capacitive circuit and I leads V S by a phase shift of Ө (which is the current angle if the source voltage is the reference signal). Ө ranges from 0 o to 90 o (0 o < Ө <90 o ). If Ө=0 o then this circuit becomes a resistive circuit and if Ө=90 o then the circuit becomes a pure capacitive circuit. C- The phase shift between the source voltage and its current Ө is important and you have two ways to find its value: = = D- Using the phasor diagram, you can find all needed quantities in the circuit like all the voltages magnitude and phase and all the currents magnitude and phase. For a parallel RC circuit, if the magnitude of I C and I R was measured in Lab. (as a peak value from an oscilloscope or rms value from a digital multimeter), then we can find the magnitude of I as follows: E- You can find all leading or lagging quantities in this circuit with respect to a reference signal like the source voltage V S. For example, it is clearly shown by the phasor diagram that I leads V S by Ө degrees, I R lags I by Ө degrees and I C leads I by 90 o - Ө. F- The phasor diagram helps in finding the change in quantities (magnitude and phase) with voltage source frequency f changing.

6 With frequency f increasing, the capacitive reactance X C will decrease and so I C will increase, the the resistor R will not be affected by the change of f and I R will not change with frequency. Since X C decrease and R is constant the total impedance Z will decrease, the source current I will increase and the admittance Y will increase. and will increase because and the tan -1 function is increasing on the interval from 0 to 90 o. In a concise way: f X C Z Y I I C Ө I R constant. G- Figure (3) below shows a time domain representation for all the vectors shown on the phasor diagram: Figure (3) Parallel RC Circuit Time Domain Representation

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